"3.something when it's empty" seems a contradiction to me. I believe that it must be 0v when it's empty, otherwise it won't be empty. The same for the supercapacitor.
That is not true.
Or rather, while it is true that a LiIon still has a trickle of energy left when it's at three volts, it's also true that said energy is not useable. Getting a LiIon to zero volts is the second-quickest way to kill it (the first being overcharging it severely).
To all intents and purposes a LiIon is therefore to be considered empty when it gets to three volts, and should not be discharged further or damage will occur.
Capacitors, on the other hand, don't care about being discharged completely.
I believe that a flashlight requires a current regulator, not a voltage regulator
LED flashlights often need more volts to run their emitters than can be provided by a single cell. Or they need less (think of lights powered by two CR123s). A voltage regulator is therefore needed.
A simple current-limiting resistor can be used if the light has a power source of close enough voltage to what is needed for the emitters.
In the case of the capacitor a resistor would not work, as the fully-charged voltage of 4.5 would drop quickly, and it'd soon be too low to fire the emitters. What would be needed would be a buck-boost voltage converter that would lower the voltage when the cap was full and boost it as it went under a certain level during discharge.
I would buy an emergency key-chain micro flashlight with 60 seconds of 1000 lumen light.
What use is a light that only lasts one minute?
The only purpose I can see for it would be to attract the attention of potential rescuers in an emergency, but the ridiculous runtime would make it poor for that purpose. What if whoever is in the general direction of your beam of light is turned the other way and turns back just after your capacitor dies?
If you foresee finding yourself in an emergency, a small hand-launched rocket flare is a much more effective way of attracting the attention of potential rescuers.
If you don't foresee that then a hyperbright light with an extremely short run time would be useless. During an emergency it's much better to have an ordinary multilevel light (such as a compact Cree flashlight powered by a primary CR123 or two), which would be useful to find your way in the dark at low power but which would also work decently for attracting attention at full blast.
Here's an even better idea: want something that'll attract attention in the dark? Get a high-power (50+mw) green portable laser.
A flashlight is not easy to see inbetween foliage, trees and whatnot, and your rescuer needs to be looking roughly in its direction to spot it in the first place. And then it could easily be ignored ("must be a hunter").
A green, bright laser beam shooting up from the forest, moving and flashing the SOS code (which everybody ought to know) is sure to attract much more attention than a small flashlight, even if capacitor-powered and super-bright.
